Figure 2.

Multidimensional triad construction. Heider Balance Theory focuses on triads—fully connected groups of three agents. We consider triads separately in each study term. If three students A, B and C communicate with each other in the considered term, they create a triad. Each of the students holds one of three opinions: in support, against (depicted as upwards or downwards arrows), unsure (depicted as a circle) on a few topics—components of multidimensional opinion vectors (the figure lists five topics). For each topic, the difference between two opposite extremist opinions is $\pm 2$ (red line), between extremist and centrist is $\pm 1$ (green line), and it is 0 (blue line) for the same opinion. The normalized to range [0, 1] sum of absolute differences between opinions over all topics is a social distance between students. If the distance is no larger than the assumed tolerance $\mathrm{\Theta }$, the edge sign is positive. Cases for different values of tolerance $\mathrm{\Theta }$ are depicted on the side panels. Left panel presents the case for the tolerance $\mathrm{\Theta }=0.4$. The tolerance is small and all edges in the multidimensional triad are negative, resulting in an unbalanced triad (depicted in red). The right panel corresponds to $\mathrm{\Theta }=0.6$. With such tolerance, students A and C are similar enough—distance between them is smaller than the tolerance—so the edge is positive. In this case, the multidimensional triad is balanced (depicted in blue).